Experiments on Instabilities and Energy Dissipation of Nonlinear Gravity-Capillary Waves

Abstract

Cross-waves are standing waves with crests perpendicular to a wave-maker; they are subharmonic waves excited by parametric instability. The modulational and chaotic behaviors of nonlinear cross-waves have been studied widely since the 1970s. Most of the previous work has focused on gravity waves where surface tension can be neglected. In this work, we study cross-waves that are highly dependent on surface tension as well as gravity. By oscillating a planar wave-maker either vertically or horizontally with frequencies of 25Hz through 40Hz at one end of a rectangular basin, two dimensional multi-component surface patterns are realized. Using the free-surface synthetic Schlieren technique to measure the surface elevations, multi-dimensional Fourier transforms are utilized to track the evolutionary spectrum of the water surface in both the temporal and spatial domains. Wavelet transforms are implemented to show the development of the various frequency components. Three-wave resonances with and without first subharmonics are observed for small nonlinearity. Three-dimensional oblique propagating cross-waves are generated at higher nonlinearity; unlike most previous cross-wave experiments, this staggered pattern propagates far downstream. Experimental evidence shows that two oblique propagating waves form a two dimensional short-crested pattern, and that the lateral component of the waves develops into parametric sloshing modes corresponding to the width of the tank. Two regimes of nonlinear wave patterns, resonant triads and oblique propagating cross-waves, are delineated.

Gravity-capillary waves play a significant role in air-sea interactions, and they exhibit much different features compared to gravity waves. They can be observed widely on the sea surface. Parasitic waves and micro-breaking can be observed on the water surface with winds, however the presence of wind makes it difficult to analyze the mechanisms of the wave itself. In this dissertation, parasitic waves and micro-breaking on gravity-capillary waves are examined experimentally, both in the absence of wind. Parasitic waves and axisymmetric micro-breaking waves are generated mechanically in a convergent channel, where energy density increases due to spatial convergence. Three experimental techniques are used to measure wave properties: planar laser induced fluorescence (PLIF), particle image velocimetry (PIV), and shadowgraphs. The wave profile evolution and vortices beneath the parasitic waves are studied. The micro-breaking of gravity-capillary waves is observed on a surface with added surfactant. Energy dissipation of parasitic waves and micro-breaking is quantified, and the enhanced dissipation caused by parasitic waves is identified through the experiments. The results yield insight into wave characteristics and energy dissipation on the air-sea interface at small scales.

A preliminary experimental study on surfactant effects on capillary wave damping is conducted. The dissipation rate with and without different types of surfactant is obtained. The results show that an insoluble surfactant, polydimethylsiloxane (PDMS), introduced more damping into the capillary wave system than soluble surfactants, for example, Triton X-100.